Solution of quadratic nonlinear problems with multiple scales Lindstedt-Poincare method

Pakdemirli M., SARI G.

Mathematical and Computational Applications, vol.20, no.2, pp.137-150, 2015 (Scopus, TRDizin) identifier

  • Publication Type: Article / Article
  • Volume: 20 Issue: 2
  • Publication Date: 2015
  • Doi Number: 10.19029/mca-2015-012
  • Journal Name: Mathematical and Computational Applications
  • Journal Indexes: Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.137-150
  • Keywords: Numerical solutions, Perturbation methods, Systems with quadratic nonlinearities
  • Manisa Celal Bayar University Affiliated: Yes

Abstract

A recently developed perturbation algorithm namely the multiple scales Lindstedt-Poincare method (MSLP) is employed to solve the mathematical models. Three different models with quadratic nonlinearities are considered. Approximate solutions are obtained with classical multiple scales method (MS) and the MSLP method and they are compared with the numerical solutions. It is shown that MSLP solutions are better than the MS solutions for the strongly nonlinear case of the considered models.